THE PEBBLE GAME.
(
Puzzle Games.)
Here is an interesting little puzzle game that I used to play with an
acquaintance on the beach at Slocomb-on-Sea. Two players place an odd
number of pebbles, we will say fifteen, between them. Then each takes in
turn one, two, or three pebbles (as he chooses), and the winner is the
one who gets the odd number. Thus, if you get seven and your opponent
eight, you win. If you get six and he gets nine, he wins. Ought the
first or second player to win, and how? When you have settled the
question with fifteen pebbles try again with, say, thirteen.
Answer:
In the case of fifteen pebbles, the first player wins if he first takes
two. Then when he holds an odd number and leaves 1, 8, or 9 he wins, and
when he holds an even number and leaves 4, 5, or 12 he also wins. He can
always do one or other of these things until the end of the game, and so
defeat his opponent. In the case of thirteen pebbles the first player
must lose if his opponent plays correctly. In fact, the only numbers
with which the first player ought to lose are 5 and multiples of 8 added
to 5, such as 13, 21, 29, etc.
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